What should I do with my father who interrupts his prayers and does not go to the mosque except for Friday prayer, and refuses advice due to personal disagreements and his anger, and should I leave him or try to discuss it with him, exposing myself to his wrath?

Prayer in the mosque with the congregation is obligatory. What your father mentioned, that the actions of some people provoke his anger, is not a legitimate excuse that permits him to miss the congregational prayer. Continue to advise him gently and wisely, choosing appropriate times. You can advise him through tapes and books, and by seeking the help of someone who has influence over him, all while supplicating for him, honoring him, and being kind to him.